Boundedness of solutions for second order differential equations with asymmetric nonlinearity

In this paper we are concerned with the boundedness of all solutions of the second order differential equationsx¨+f(x˙)+ax+−bx−+g(x)=p(t), where (a,b)(a,b) does not lie on one of the Fučik spectrum curves, the functions f and g are bounded, and p is 2π-periodic.